Time preference and productivity: observations in a growth model with heterogeneous agents

We consider an infinite-horizon economy populated by finitely many agents, each of whom acts as a worker, consumer, and entrepreneur. The agents are heterogeneous both with respect to their preferences and their technologies. Agents who demand more production inputs than they own can rent the required amounts on competitive factor markets, whereby the rental of capital is subject to a collateral constraint. Generically, there exists a unique steady state equilibrium and it is locally determinate. If the collateral constraint is sufficiently weak, only the most productive agent produces. As the collateral constraint becomes more stringent, it is still the case that only a single agent produces but it need not be the most productive one. The paper studies how time preference and productivity jointly determine the identity of the producing agent.